Interest rates model

This page describes how Equilibrium calculates interest rates on the loans in the system.


The problem of pricing a collateralised loan comes from the realms of traditional finance and stock loans. Associated research on this was pioneered by Xia and Zhou (2007). Under the Black–Scholes model, they derived a closed-form pricing formula for the infinite-maturity stock loan by solving the related optimal stopping problem. Equilibrium adapts the approach proposed by Xia and Zhou, and comes up with an elegant pricing solution that depends on borrower portfolio risk and the level of portfolio collateralization.

Interest rateLeverage(Portfolio volatilityScale factor)Interest\ rate \approx Leverage * (Portfolio\ volatility * Scale\ factor)

The interest that borrowers pay gets redistributed across the system components. The following breakdown applies:

Interest rate componentValue

Base Lender Rate

0.5% APR

Base Insurance Rate

1.0% APR

Base Treasury Rate

1.0% APR

Primary Borrower Rate

~ Leverage * Volatility

Lender share

30% of Primary Borrower Rate

Bailsman share

70% of Primary Borrower Rate

So the minimum possible interest rate borrowers pay is 2.5% APR, while the biggest contributor to the final interest rate figure is the Primary Borrower Rate which depends on the leverage the borrower undertakes and the risk (volatility) of the borrower portfolio. 30% of the Primary Borrower Rate is funnelled to lenders, while 70% is funnelled to insurers (bailsmen).

The base treasury rate is split among treasury and collators in a 50 / 50 proportion, so collators earn a 0.5% APR on top of their trx. fees rewards. Assuming the default values for risk parameters, here's the approximate interest rate breakdown (how much borrowers pay to bailsmen and lenders respectively) for a borrower portfolio, given its leverage and volatility.

Further improvements to the pricing model may include adapting the jump diffusion process to model the collateral risk, as well as adapting the model to account for margin calls and LTV requirements. This is subject of our ongoing R&D work.

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